UGKS and UGKWP Methods for Multiscale Simulation of Electrostatic Plasma in Quasineutral and Hydrodynamic Limits

Abstract

This study extends the Unified Gas-Kinetic Scheme (UGKS) and the Unified Gas-Kinetic Wave-Particle (UGKWP) method for electrostatic plasma modeling, ensuring the correct asymptotic limits with respect to both the Debye length and the mean free path. By coupling collision and transport processes within the numerical flux, the proposed approach effectively removes the hydrodynamic-limit constraint associated with the mean free path. In addition, a reformulated Poisson equation, coupled with the macroscopic moment equations, is introduced to overcome the inefficiency of the standard Poisson formulation in the quasineutral regime. The accuracy and asymptotic consistency of the proposed schemes are verified through several benchmark tests, including linear and nonlinear Landau damping and the bump-on-tail instability. The results demonstrate that the methods robustly capture plasma dynamics across hydrodynamic and quasineutral regimes, without resolution constraints imposed by either the Debye length or the mean free path.